Hairspring Polynomial Geometry for Isochronism
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Solution Overview
Problem
Existing mechanical watch hairsprings face issues with isochronism due to the mismatch between the center of gravity and the center of rotation, leading to eccentric deformations and anisochronism, with previous solutions like the Breguet Philips curve and angle hairspring not fully addressing the problem of center alignment during expansions and contractions.
Innovation Solution
A method involving a continuous polynomial function to define the radius and thickness of the hairspring along its entire length, ensuring the geometric center coincides with the center of gravity, using specific polynomial equations to optimize coefficients and minimize displacement during expansions and contractions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a conventional hairspring geometry is used, then the manufacturing process is simple, but the center of gravity does not coincide with the center of rotation, causing eccentric deformations and anisochronism
Solution Approach 1:
The patent applies parameter changes by modifying the geometric parameters of the hairspring through polynomial functions. The radius, thickness, and width of the hairspring are defined as continuous polynomial functions of the angle, allowing precise control over the mass distribution to align the center of gravity with the center of rotation while maintaining manufacturability.
Solution Approach 2:
The patent implements local quality by varying the thickness and width of the hairspring at different angular positions according to polynomial functions. This allows specific regions of the hairspring to have different properties, concentrating mass in ways that align the center of gravity with the center of rotation while keeping the overall design practical.
2Reliability
If the hairspring expands and contracts during operation, then it performs its regulating function, but the center of gravity displaces, disrupting adjustment and making the balance-spring anisochronous
Solution Approach 1:
The patent uses parameter changes by defining the hairspring geometry through polynomial functions that account for expansion and contraction behavior. The continuous polynomial definitions of radius, thickness, and width ensure that the center of gravity remains aligned with the center of rotation even as the hairspring changes size during operation, maintaining isochronism.
Solution Approach 2:
The patent applies dynamics by designing the hairspring geometry to adapt to its dynamic expansion and contraction during operation. The polynomial function definitions allow the mass distribution to remain optimized throughout the range of motion, ensuring the center of gravity stays aligned with the center of rotation regardless of the hairspring's state.
3Manufacturing precision
If previous solutions like Breguet Philips curve or angle hairspring are used, then some improvement in center alignment is achieved, but they do not fully address the problem of center alignment during expansions and contractions
Solution Approach 1:
The patent improves upon previous solutions by using continuous polynomial functions to define the hairspring geometry, allowing for more precise control over mass distribution. This approach provides better alignment of the center of gravity with the center of rotation during both static and dynamic conditions, while the polynomial formulation maintains practical manufacturability.
Solution Approach 2:
The patent applies preliminary action by pre-calculating and embedding the optimal mass distribution into the hairspring geometry through polynomial functions. This preliminary design ensures that the center of gravity alignment is achieved before the hairspring is put into operation, accounting for expected expansion and contraction behavior in advance.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly improves isochronism by maintaining the center of gravity alignment, reducing pivot reaction forces and achieving greater stability in the balance spring's rate, with variations in rate and center of gravity displacement minimized, resulting in improved performance compared to traditional designs.
Implementation Method 1
the turns of a flat hairspring deform eccentrically when the hairspring is working, due to the fact that the center of gravity of the hairspring does not initially correspond to the center of rotation of the balance-spring and/or due to the displacement of the center of gravity during the expansions/contractions of the hairspring
Data Source
Figure 1
Figure 2
Figure 3a~3d
AI summary
The method involves characterizing length of a spiral shape that passes through a curve representing three points set by position and geometry of attachment units of a hairspring. The three points are defined by an attachment of the spring to a ring, a penultimate turn intended to be located next to a stud, and a last turn that is to be attached to the stud. A function defining thickness of the spiral shape is defined, and coefficients of a polynomial function and the function are optimized by calculations and simulations.